The goal of our research is the non-invasive quantification of myocardial blood flow (in ml/min per g of tissue) with magnetic resonance (MR) imaging during the first pass of an MR contrast agent. For accurate estimation of blood a multi-pathway, axially distributed model of capillary tissue exchange (MMID4) developed at the National Simulation Resource is applied to the analysis of the first pass residue curves to determine myocardial blood flow. The concepts for the quantification with MR of myocardial blood flow are being validated in animal models, where flow measurements with radio-isotope labeled microspheres are used as gold standard reference. Both extracellular and intravascular contrast agents are used to determine, not only blood flow, but also blood volume (with intravascular contrast agents), the capillary permeability (with extracellular contrast agents), and the relation between flow and the capillary permeability surface area product (2). The insights from these studies are being applied for the non-invasive quantification of blood flow in patients.